, Volume 43, Issue 1, pp 41–52 | Cite as

Designing representations of trigonometry instruction to study the rationality of community college teaching

  • Vilma Mesa
  • Patricio Herbst
Original Article


We describe the process followed to design representations of mathematics teaching in a community college. The end product sought are animated videos to be used in investigating the practical rationality that community college instructors use to justify norms of the didactical contract or possible departures from those norms. We have chosen to work within the trigonometry course, in the context of an instructional situation, “finding the values of trigonometric functions,” and specifically on a case of this situation that occurs as instructors and students are working on examples on the board. We describe the design of the material needed to produce the animations: (1) identifying an instructional situation, (2) identifying norms of the contract that are key in that situation, (3) selecting or creating a scenario that illustrates those norms, (4) proposing alternative scenarios that instantiate breaches of those norms, and (5) anticipating justifications or rebuttals for the breaches that could be found in instructors’ reactions. We illustrate the interplay of contextual and theoretical elements as we make decisions and state hypothesis about the situation that will be prototyped.


Representation of teaching Community colleges Trigonometry Didactical contract Classroom interaction Teacher thinking Teaching practice 



The research reported in this article is supported by the National Science Foundation grants DRL-0745474 to the first author and ESI-0353285 to the second author. Opinions expressed here are the sole responsibility of the authors and do not reflect the views of the foundation.


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Copyright information

© FIZ Karlsruhe 2010

Authors and Affiliations

  1. 1.3111 SEB School of EducationUniversity of MichiganAnn ArborUSA
  2. 2.4119 SEB School of EducationUniversity of MichiganAnn ArborUSA

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